cho \(0\le a\le b\le c\le1\) . Tìm GTLN của

\(Q=a^2\left(b-c\right)+b^2\left(c-b\right)+c^2\left(1-c\right)\)

cho x,y > 0. Cmr: \(x^2\left(y-x\right)\le\frac{4y^3}{27}\)

cho a,b,c> 0 thỏa mãn \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=1\) . Tìm GTNN của \(A=\left(1+a^2\right)\left(1+b^2\right)\left(1+c^2\right)\)

cho a,b,c> 0 . Cmr:

\(2\left(\frac{a}{b+2c}+\frac{b}{c+2a}+\frac{c}{a+2b}\right)\ge1+\frac{b}{b+2a}+\frac{c}{c+2b}+\frac{a}{a+2c}\)

cho a, b, c > 0 thỏa mãn a+b+c=3. Cmr:

\(\frac{a+1}{b^2+1}+\frac{b+1}{c^2+1}+\frac{c+1}{a^2+1}\ge3\)